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Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence

Werndl, Charlotte and Frigg, Roman (2015) Reconceptualising equilibrium in Boltzmannian statistical mechanics and characterising its existence. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 49. pp. 19-31. ISSN 1355-2198

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Identification Number: 10.1016/j.shpsb.2014.12.002

Abstract

In Boltzmannian statistical mechanics macro-states supervene on microstates. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is singled out as the equilibrium region of the system. What justifies this association? We review currently available answers to this question and find them wanting both for conceptual and for technical reasons. We propose a new conception of equilibrium and prove a mathematical theorem which establishes in full generality – i.e. without making any assumptions about the system’s dynamics or the nature of the interactions between its components – that the equilibrium macro-region is the largest macro-region. We then turn to the question of the approach to equilibrium, of which there exists no satisfactory general answer so far. In our account, this question is replaced by the question when an equilibrium state exists. We prove another – again fully general – theorem providing necessary and sufficient conditions for the existence of an equilibrium state. This theorem changes the way in which the question of the approach to equilibrium should be discussed: rather than launching a search for a crucial factor (such as ergodicity or typicality), the focus should be on finding triplets of macro-variables, dynamical conditions, and effective state spaces that satisfy the conditions of the theorem.

Item Type: Article
Official URL: http://www.journals.elsevier.com/studies-in-histor...
Additional Information: © 2015 Elsevier Ltd.
Divisions: Philosophy, Logic and Scientific Method
CPNSS
Centre for Analysis of Time Series
Subjects: B Philosophy. Psychology. Religion > BC Logic
H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Philosophy, Logic and Scientific Method
Research centres and groups > Centre for Philosophy of Natural and Social Science (CPNSS)
Research centres and groups > Centre for the Analysis of Time Series (CATS)
Date Deposited: 23 Jan 2015 11:19
Last Modified: 25 Feb 2016 13:35
URI: http://eprints.lse.ac.uk/id/eprint/60786

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